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A relaxed proximal point algorithm with double-inertial effects for nonconvex equilibrium problems

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arXiv 2025年

作者： Tran, Van Nam Faculty of Applied Sciences Ho Chi Minh City University of Technology and Education Ho Chi Minh City Viet Nam

In this paper, we present a relaxation proximal point method with double inertial effects to approximate a solution of a non-convex equilibrium problem. We give global convergence results of the iterative sequence generated by our algorithm. Some known results are recovered as special cases of our results. Numerical test is given to support the theoretical findings. © 2025, CC BY.

关键词： consensus algorithm

FROM DESCRIPTIVE TO DISTRIBUTED

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arXiv 2025年

作者： Grebík, Jan Vidnyánszky, Zoltán Faculty of Informatics Masaryk University Botanicka 68A 60200 Brno Czech Republic Eötvös Loránd University Institute of Mathematics Pázmány Péter stny. 1/C 1117 Budapest Hungary

In the past couple of years a rich connection has been found between the fields of descriptive set theory and distributed computing. Frequently, and less surprisingly, finitary algorithms can be adopted to the infinite setting, resulting in theorems about infinite, definable graphs. In this survey, we take a different perspective and illustrate how results and ideas from descriptive set theory provide new insights and techniques to the theory of distributed computing. We focus on the two classical topics from graph theory, vertex and edge colorings. After summarizing the up-to-date results from both areas, we discuss the adaptation of Marks’ games method to the LOCAL model of distributed computing and the development of the multi-step Vizing’s chain technique, which led to the construction of the first non-trivial distributed algorithms for Vizing colorings. We provide a list of related open problems to complement our discussion. Finally, we describe an efficient deterministic distributed algorithm for Brooks coloring on graphs of subexponential growth. © 2025, CC BY.

关键词： consensus algorithm

A Blockchain-Based Approach to WoT Device Access Control

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A Blockchain-Based Approach to WoT Device Access Control

Computational Intelligence Approaches and Applications (ICCIAA), International Conference on

作者： Someah Alangari Computer Science Department College of Computing and IT Shaqra University Shaqra Saudi Arabia

ISBN: (数字)9798331523657

ISBN: (纸本)9798331523664

The Web of Things (WoT) represents an interconnected network of sensors and smart devices. It faces significant security and privacy challenges, including potential data breaches, unauthorized access issues, and concerning scalability problems. This paper introduces a blockchain-based solution that aims to enhance the security and reliability of the WoT. Taking advantage of the inherent transparency of blockchain's distributed ledger, the elimination of single points of failure through consensus algorithms, the enforcement of access control and privacy through smart contracts, and the assurance of data confidentiality through encryption, I propose an innovative design for the WoT that could guarantee enhanced security and trust. I also incorporate the use of a homomorphic hash function to further boost data privacy and integrity. This paper presents a comprehensive framework that employs blockchain technology to transform the current WoT into a more secure and trusted network, which I term the “Web of Trust”.

关键词： Access control Data privacy Distributed ledger Scalability consensus algorithm Computer architecture Transforms Standardization Blockchains Encryption

On the Locality of the Lovász Local Lemma

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arXiv 2025年

作者： Davies-Peck, Peter Durham University United Kingdom

The Lovász Local Lemma is a versatile result in probability theory, characterizing circumstances in which a collection of n ‘bad events’, each occurring with probability at most p and dependent on a set of underlying random variables, can be avoided. It is a central tool of the probabilistic method, since it can be used to show that combinatorial objects satisfying some desirable properties must exist. While the original proof was existential, subsequent work has shown algorithms for the Lovász Local Lemma: that is, in circumstances in which the lemma proves the existence of some object, these algorithms can constructively find such an object. One main strand of these algorithms, which began with Moser and Tardos’s well-known result (JACM 2010), involves iteratively resampling the dependent variables of satisfied bad events until none remain satisfied. In this paper, we present a novel analysis that can be applied to resampling-style Lovász Local Lemma algorithms. This analysis shows that an output assignment for the dependent variables of most events can be determined only from O(log log1/p n)-radius local neighborhoods, and that the events whose variables may still require resampling can be identified from these neighborhoods. This allows us to improve randomized complexities for the constructive Lovász Local Lemma (with polynomial criterion) in several parallel and distributed models. In particular, we obtain: • A LOCAL algorithm with O(log log1/p n) node-averaged complexity (while matching the O(log1/p n) worst-case complexity of Chung, Pettie, and Su). • An algorithm for the LCA and VOLUME models requiring dO(log log1/p n) probes per query. • An O(log log log1/p n)-round algorithm for CONGESTED CLIQUE, linear space MPC, and Heterogenous MPC. © 2025, CC BY.

关键词： consensus algorithm

A fast algorithm for the Frobenius problem in three variables

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arXiv 2025年

作者： Rosin, Daniel

Given the function Γ(X) = a1x1 + a2x2 + a3x3, where the set {a1, a2, a3}, denoted A, consists of positive integers and the set {x1, x2, x3}, denoted X, consists of non-negative integers, the Frobenius problem in three variables is to find the greatest integer, which is not in the codomain of Γ. The fastest known algorithm for solving the three variable case of the Frobenius problem was invented by H. Greenberg in 1988 whose worst case time complexity is a logarithmic function of A. In 2017 A. Tripathi presented another algorithm for solving the same problem. This article presents an algorithm whose foundation is the same as Tripathi’s. However, this algorithm is significantly different from Tripathi’s and we show that its worst case time complexity is also a logarithmic function of *** Codes 11D07 © 2025, CC BY.

关键词： consensus algorithm

Runtime Analysis of the Compact Genetic algorithm on the LeadingOnes Benchmark

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arXiv 2025年

作者： Chwialkowski, Marcel Doerr, Benjamin Krejca, Martin S. École Polytechnique Institut Polytechnique de Paris Palaiseau France Palaiseau France

The compact genetic algorithm (cGA) is one of the simplest estimation-of-distribution algorithms (EDAs). Next to the univariate marginal distribution algorithm (UMDA)—another simple EDA—, the cGA has been subject to extensive mathematical runtime analyses, often showcasing a similar or even superior performance to competing approaches. Surprisingly though, up to date and in contrast to the UMDA and many other heuristics, we lack a rigorous runtime analysis of the cGA on the LEADINGONES benchmark—one of the most studied theory benchmarks in the domain of evolutionary computation. We fill this gap in the literature by conducting a formal runtime analysis of the cGA on LEADINGONES. For the cGA’s single parameter—called the hypothetical population size—at least polylogarithmically larger than the problem size, we prove that the cGA samples the optimum of LEADINGONES with high probability within a number of function evaluations quasi-linear in the problem size and linear in the hypothetical population size. For the best hypothetical population size, our result matches, up to polylogarithmic factors, the typical quadratic runtime that many randomized search heuristics exhibit on LEADINGONES. Our analysis exhibits some noteworthy differences in the working principles of the two algorithms which were not visible in previous works. © 2025, CC BY.

关键词： consensus algorithm

Convergence Analysis of the Wasserstein Proximal algorithm beyond Geodesic Convexity

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arXiv 2025年

作者： Zhu, Shuailong Chen, Xiaohui Section of Computer Science Ecole Polytechnique Fédérale de Lausanne Switzerland Department of Mathematics University of Southern California United States

The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent progress in studying the training dynamics of the noisy gradient descent algorithm on two-layer neural networks in the mean-field regime, we provide in this paper a simple and self-contained analysis for the convergence of the general-purposeWasserstein proximal algorithm without assuming geodesic convexity of the objective functional. Under a natural Wasserstein analog of the Euclidean Polyak-Lojasiewicz inequality, we establish that the proximal algorithm achieves an unbiased and linear convergence rate. Our convergence rate improves upon existing rates of the proximal algorithm for solving Wasserstein gradient flows under strong geodesic convexity. We also extend our analysis to the inexact proximal algorithm for geodesically semiconvex objectives. In our numerical experiments, proximal training demonstrates a faster convergence rate than the noisy gradient descent algorithm on mean-field neural networks. © 2025, CC BY-NC-SA.

关键词： consensus algorithm

Single-Loop Variance-Reduced Stochastic algorithm for Nonconvex-Concave Minimax Optimization

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arXiv 2025年

作者： Jiang, Xia Zhu, Linglingzhi Zheng, Taoli So, Anthony Man-Cho Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Hong Kong

Nonconvex-concave (NC-C) finite-sum minimax problems have broad applications in decentralized optimization and various machine learning tasks. However, the nonsmooth nature of NC-C problems makes it challenging to design effective variance reduction techniques. Existing vanilla stochastic algorithms using uniform samples for gradient estimation often exhibit slow convergence rates and require bounded variance assumptions. In this paper, we develop a novel probabilistic variance reduction updating scheme and propose a single-loop algorithm called the probabilistic variance-reduced smoothed gradient descent-ascent (PVR-SGDA) algorithm. The proposed algorithm achieves an iteration complexity of O(∊−4), surpassing the best-known rates of stochastic algorithms for NC-C minimax problems and matching the performance of the best deterministic algorithms in this context. Finally, we demonstrate the effectiveness of the proposed algorithm through numerical simulations. Copyright © 2025, The Authors. All rights reserved.

关键词： consensus algorithm

On distributed consensus algorithms and their application to power sharing in DC microgrids

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On distributed consensus algorithms and their application to...

International Conference on System Theory, Control, and Computing (ICSTCC)

作者： Chris Zevenbergen Sergio Grammatico Delft Center for Systems and Control TU Delft The Netherlands

ISBN: (数字)9781728198095

ISBN: (纸本)9781728198101

We consider nonlinear consensus algorithms and their application to proportional power sharing in DC microgrids. We show that a power sharing algorithm is a special case of nonlinear consensus protocol and we establish convergence to state consensus with adaptive gains. The key facts are the presence of an agreement function in the power sharing algorithm and the preservation of a weighted geometric mean over time. These observations allow us to improve the performance of this class of algorithms via the theory of nonlinear consensus.

关键词： Microgrids consensus protocol Voltage control Energy resources consensus algorithm Power system stability Lyapunov methods